A new class of bathtub-shaped hazard rates and its application in a comparison of two test-statistics

A class of life distributions arising in reliability situations has bathtub shaped hazard rates. The author investigates the problem of testing exponentiality (constant hazard rate) against bathtub distributions. A critical note on well-known bathtub distributions is made from a practical point of view, and a class of bathtub-distributions is introduced that is extremal in the context of power investigations. A Monte Carlo power comparison of two test-statistics is performed. The presentation is based on the total time on test concept